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楼主: moranhuishou

发现3个超级完美数

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 楼主| 发表于 2009-12-12 13:43 | 显示全部楼层

发现3个超级完美数

下面引用由kanyikan2009/12/12 10:46am 发表的内容:
4倍的,10000000内只发现以下3个,5以及5倍以上的没发现。
30240,32760,2178540
很好很好。
初步猜想,不一定会有除了2^n之外还有5以及5倍以上的。
 楼主| 发表于 2009-12-12 14:04 | 显示全部楼层

发现3个超级完美数

有朋友发帖:(看来11楼观点有误)
4倍完全数有:30240:
5倍完全数有::14182439040。
发表于 2009-12-12 14:44 | 显示全部楼层

发现3个超级完美数

http://mathworld.wolfram.com/MultiperfectNumber.html
发表于 2009-12-12 15:42 | 显示全部楼层

发现3个超级完美数

我不懂什么英文,不过从kanyikan提供的链接上,能看出那个网站是专门研究因子和的。我查找一下在维基百科上,看是否有中文这方面的资料。
 楼主| 发表于 2009-12-12 18:26 | 显示全部楼层

发现3个超级完美数


Number Theory > Special Numbers > Divisor-Related Numbers >
Recreational Mathematics > Mathematical Records >

Multiperfect Number
  


A number  is -multiperfect (also called a -multiply perfect number or -pluperfect number) if

for some integer , where  is the divisor function. The value of  is called the class. The special case  corresponds to perfect numbers , which are intimately connected with Mersenne primes (Sloane';s A000396). The number 120 was long known to be 3-multiply perfect () since

The following table gives the first few  for , 3, ..., 6.
2 A000396 6, 28, 496, 8128, ...
3 A005820 120, 672, 523776, 459818240, 1476304896, 51001180160
4 A027687 30240, 32760, 2178540, 23569920, ...
5 A046060 14182439040, 31998395520, 518666803200, ...
6 A046061 154345556085770649600, 9186050031556349952000, ...

谢谢kanyikan提供的宝贵资料。
发表于 2009-12-12 18:36 | 显示全部楼层

发现3个超级完美数

    楼主善于编程,很多的想法可及时验证,实在可喜可贺!更为钦羡,,,于鄙,只有钦羡的份-------永不可企及!胡言乱语,顶贴,以贺!
发表于 2009-12-12 19:54 | 显示全部楼层

发现3个超级完美数

楼主是才子,
             ---- 不可小觑也!
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\frac{\square}{\square}\sqrt{\square}\square_{\baguet}^{\baguet}\overarc{\square}\ \dot{\baguet}\left(\square\right)\binom{\square}{\square}\begin{cases}\square\\\square\end{cases}\ \begin{bmatrix}\square&\square\\\square&\square\end{bmatrix}\to\Rightarrow\mapsto\alpha\ \theta\ \pi\times\div\pm\because\angle\ \infty
\frac{\square}{\square}\sqrt{\square}\sqrt[\baguet]{\square}\square_{\baguet}\square^{\baguet}\square_{\baguet}^{\baguet}\sum_{\baguet}^{\baguet}\prod_{\baguet}^{\baguet}\coprod_{\baguet}^{\baguet}\int_{\baguet}^{\baguet}\lim_{\baguet}\lim_{\baguet}^{\baguet}\bigcup_{\baguet}^{\baguet}\bigcap_{\baguet}^{\baguet}\bigwedge_{\baguet}^{\baguet}\bigvee_{\baguet}^{\baguet}
\underline{\square}\overline{\square}\overrightarrow{\square}\overleftarrow{\square}\overleftrightarrow{\square}\underrightarrow{\square}\underleftarrow{\square}\underleftrightarrow{\square}\dot{\baguet}\hat{\baguet}\vec{\baguet}\tilde{\baguet}
\left(\square\right)\left[\square\right]\left\{\square\right\}\left|\square\right|\left\langle\square\right\rangle\left\lVert\square\right\rVert\left\lfloor\square\right\rfloor\left\lceil\square\right\rceil\binom{\square}{\square}\boxed{\square}
\begin{cases}\square\\\square\end{cases}\begin{matrix}\square&\square\\\square&\square\end{matrix}\begin{pmatrix}\square&\square\\\square&\square\end{pmatrix}\begin{bmatrix}\square&\square\\\square&\square\end{bmatrix}\begin{Bmatrix}\square&\square\\\square&\square\end{Bmatrix}\begin{vmatrix}\square&\square\\\square&\square\end{vmatrix}\begin{Vmatrix}\square&\square\\\square&\square\end{Vmatrix}\begin{array}{l|l}\square&\square\\\hline\square&\square\end{array}
\to\gets\leftrightarrow\nearrow\searrow\downarrow\uparrow\updownarrow\swarrow\nwarrow\Leftarrow\Rightarrow\Leftrightarrow\rightharpoonup\rightharpoondown\impliedby\implies\Longleftrightarrow\leftharpoonup\leftharpoondown\longleftarrow\longrightarrow\longleftrightarrow\Uparrow\Downarrow\Updownarrow\hookleftarrow\hookrightarrow\mapsto
\alpha\beta\gamma\Gamma\delta\Delta\epsilon\varepsilon\zeta\eta\theta\Theta\iota\kappa\varkappa\lambda\Lambda\mu\nu\xi\Xi\pi\Pi\varpi\rho\varrho\sigma\Sigma\tau\upsilon\Upsilon\phi\Phi\varphi\chi\psi\Psi\omega\Omega\digamma\vartheta\varsigma\mathbb{C}\mathbb{H}\mathbb{N}\mathbb{P}\mathbb{Q}\mathbb{R}\mathbb{Z}\Re\Im\aleph\partial\nabla
\times\cdot\ast\div\pm\mp\circ\backslash\oplus\ominus\otimes\odot\bullet\varnothing\neq\equiv\not\equiv\sim\approx\simeq\cong\geq\leq\ll\gg\succ\prec\in\ni\cup\cap\subset\supset\not\subset\not\supset\notin\not\ni\subseteq\supseteq\nsubseteq\nsupseteq\sqsubset\sqsupset\sqsubseteq\sqsupseteq\sqcap\sqcup\wedge\vee\neg\forall\exists\nexists\uplus\bigsqcup\bigodot\bigotimes\bigoplus\biguplus\bigcap\bigcup\bigvee\bigwedge
\because\therefore\angle\parallel\perp\top\nparallel\measuredangle\sphericalangle\diamond\diamondsuit\doteq\propto\infty\bowtie\square\smile\frown\bigtriangledown\triangle\triangleleft\triangleright\bigcirc \wr\amalg\models\preceq\mid\nmid\vdash\dashv\nless\ngtr\ldots\cdots\vdots\ddots\surd\ell\flat\sharp\natural\wp\clubsuit\heartsuit\spadesuit\oint\lfloor\rfloor\lceil\rceil\lbrace\rbrace\lbrack\rbrack\vert\hbar\aleph\dagger\ddagger

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